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Question: The area of the region bounded by y = e<sup>x</sup>, y = e<sup>–x</sup>, x = 0 and x = 1 is-...

The area of the region bounded by y = ex, y = e–x, x = 0 and

x = 1 is-

A

e +1e\frac { 1 } { \mathrm { e } }

B

log (4/e)

C

4 log (4/e)

D

e +1e\frac { 1 } { \mathrm { e } }– 2

Answer

e +1e\frac { 1 } { \mathrm { e } }– 2

Explanation

Solution

A = ∫01(ex−e−x)dx\int _ { 0 } ^ { 1 } \left( e ^ { x } - e ^ { - x } \right) d x

̃ A = (ex + e–x)01

A = (e + e–1) – (1 + 1)

A = e + 1e\frac { 1 } { \mathrm { e } } –2